Copyright 1999, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 1999 SPE Asia Pacific Oil and GasConference and Exhibition held in Jakarta, Indonesia, 20–22 April 1999.

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AbstractThe Spraberry Trend Area in west Texas presents unusualproblems for both primary production and waterflooding.Primary production under solution gas drive recovered lessthan 10% of the oil in place. After more than 40 years ofwaterflooding the current oil recovery is still less than 12%.In order to improve the reservoir performance in theSpraberry Trend Area, our studies focused oncharacterization, modeling and simulation of the HumbleWaterflood Pilot. A pilot model was constructed using athree-phase, three-dimensional, dual porosity simulator(ECLIPSE).Lack of understanding of two key issues are addressed,stress-sensitive permeability and rock wettability. Theseparameters appear to have a dominant effect in reservoirperformance. This study emphasized detailed analysis of thestress-sensitive option used in the simulator by developing anumerical model of solid deformation and stress-pressuredependent permeability using a fully implicit finite-difference scheme. The numerical modeling of spontaneousand forced imbibition experiments using Spraberry coreplugs were also conducted to investigate the wettability ofthe Spraberry matrix. These analyses may be helpfulfor understanding reservoir behavior and reducing uncertainparameters.Several studies were conducted after successfully matchingwaterflood pilot performance. The waterflood pilot model

• Now at The Harold Vance Department of PetroleumEngineering, Texas A&M University, College Station, TX77843-3116, e-mail; schech@spindletop.tamu.edu

was applied to run a series of sensitivity simulations forhorizontal wells, well injectivity optimization, cyclicwaterflooding, and other scenarios that could be useful toincrease reservoir productivity. Based on results ofwaterflood pilot scenarios, this study may be able to provideguidelines for field development in the Spraberry TrendArea.

IntroductionNaturally fractured reservoirs behave in a significantly

different manner from homogeneous reservoirs, due to theexistence of two media, matrix and fractures. The matrixsystem is relatively tight with insignificant permeability. Incontrast, fractures have high permeability but havesignificantly low porosity. The matrix system, which is thefluid storage element in the fractured reservoirs, feeds thefractures that are responsible for transport throughout thereservoir. The fractures not only enhance the overallpermeability, but also create significant permeabilityanisotropy. Knowledge of the imbibition transfer,orientation and magnitude of fracture permeabilityanisotropy is important in developing and managing thereservoir. There is no established methodology available inthe literature for developing a thin pay zone and complex,naturally fractured reservoir with low matrix permeabilityand an extensive set of fractures.

This paper describes a methodology developed for thecharacterization of the Spraberry field, a naturally fracturedreservoir in west Texas through the interpretation of theHumble waterflood pilot performance. The Spraberry TrendArea was discovered in January 1949. The field is mainlycomposed of sandstone, shale, siltstone and limestone. Themask of the rock is divided into three distinct units: theUpper Spraberry, a sandy zone; the Middle Spraberry, azone of shales and limestones; and the Lower Spraberry,another sandy zone. The individual beds rarely exceed 15 ftin thickness. Reservoir characterization demonstrated thatthe productive oil sands in the Upper Spraberry consist oftwo thin intervals, the 1U and 5U. The field covers about400,000 acres and is a naturally fractured and solution gasdrive reservoirs (Fig. 1).

In addition to being one of the world’s largest fields inareal extent, the Spraberry Trend is considered one of the

SPE 54336

Reservoir Simulation of a Waterflood Pilot in the Naturally Fractured Spraberry TrendErwinsyah Putra, SPE, ITB/New Mexico Institute of Mining and Technology, David S. Schechter •, SPE, New MexicoInstitute of Mining and Technology

2 E. PUTRA, D.S. SCHECHTER SPE 54336

richest oil provinces in the world. However, the Spraberryfield presents unusual problems for both primary andsecondary recoveries. Primary recovery, which wasdominated by capillary retention of oil in the matrix blocks,was less than 10% of the oil in place. Well productivitydeclined rapidly after the fracture system was depleted.Along with a rapid decline in well productivity, the gas-oilratio increased rapidly, since primary recovery wasdominated by solution gas drive.

After a series of laboratory experiments, a waterfloodpilot was started on March 8, 1955. The displacement of oilby waterflooding was proved successful in this pilot. Fromthis result, large-scale waterflooding was initiated in theSpraberry Trend. After more than 40 years of waterflooding,the current oil recovery is still less than 12%. The reasonsfor its low productivity and disappointing waterfloodperformance have remained unexplained until now. Varioushypotheses have been proposed to explain the poorperformance of wide-scale waterflooding. These hypothesesinclude: lack of pattern confinement and injection welldensity, incorrect well pattern alignment, fracturemineralization, lack of understanding the imbibition transfermechanism and stress-sensitive permeability.

Two key issues that are the causes of low productivitywere addressed in this study prior to modeling andsimulation of the Humble Pilot; the stress-sensitivepermeability and the imbibition mechanism. Through thesetwo studies, the quality and quantity of the simulation datawere enhanced. These studies also helped to conservevaluable data and information from the laboratoryexperiments. Information from geological and petrophysicalanalysis, core-log integration, fracture characterization, andextensive data available on a well-by-well basis wereintegrated to build the reservoir model and to simulate thewaterflood pilot performance. When interpretation of thispilot is finished, an understanding will be gained that willaid in current plans for expanded process options. This pilotmodel can also be used in the future to simulate horizontalwells and CO2 injection and combinations of thesetechnologies.

Stress-Sensitive Rock PropertiesBackground. Fractures are the main fluid flow paths innaturally fractured reservoirs. Therefore, the productivity ofnaturally fractured reservoirs relies on the magnitude offracture permeability. When pore pressure depletes due toexcessive oil/gas production rates in highly stress-sensitiverock properties, the confining stresses on the reservoir rockincrease, causing compaction of the rock. The interactionbetween fluid flow and rock volumetric deformation causessignificant reduction in fracture permeability. This, in turn,may reduce the reservoir productivity. Evidence fromseveral sources indicates that Spraberry wells are stress-sensitive.1,2 This evidence provided the primary motivationto study stress sensitivity in detail.

In modeling stress sensitivity, current conventional dual-porosity simulators treat permeability and porosity as a

function of pore pressure and neglect the effect of rockdeformation due to changing of the stress-state. Hence,productivity predictions obtained using conventional dual-porosity simulators in reservoirs with stress-sensitivepermeability may be misleading. Therefore, a numericalmodel of a stress dual-porosity simulator was developed inthis study to take into account the effect of soliddeformation in naturally fractured reservoirs.Numerical Modeling. Although naturally fracturedreservoirs have been the subject of much research, fewstudies investigate the effect of solid deformation on thechanges in fluid pressure. Because this topic is still beingactively researched, uncertainties exist in the governingequation describing this process, as shown by the citedreferences.3-6 The governing equation used in this research isadopted from Chen and Teufel (1997),6 which is consideredconceptually more consistent than other cited references.

The governing equation for fluid flow and the effect ofsolid deformation on the change of fluid pressure can bewritten as 6,7 :For the matrix system:

Γµ

−∂∇∂

+∂

∂+

∂∂

=∇⋅∇t

)u.(b

tp

bt

pb)p

k( 13

212

1111

1 (1)

For the fracture system:

Γµ

+∂∇∂

+∂

∂+

∂∂

=∇⋅∇t

)u.(b

tp

bt

pb)p

k( 23

222

1212

2 (2)

For the linear elastic of isotropic porous material:

i

22

i

11

ii

2xp

xp

x)u(

21G

uG∂∂

+∂∂

=∂

⋅∇∂−

+∇ ααν

............ (3)

where the coefficients are represented by:

)(ccb 111p11111 αβφφ −+= )(cb 221p112 αβφ −=

b

1p113 c

cb

φ= )(cb 112p221 αβφ −=

)(cb 222p222 αβφ −=b

2p223 c

cb

φ=

1

**

1pb

cc

φ

α= )cc(c *

pp2

t2p −=

φφ

φα b

pc

c =b

**

1 c

cb

αα =

b

**

2 c

cb

ααα −=

b

scc

1 −=α

p

scc

1 −=βp

**p

1 c

c ββ =

12 βββ −=

SPE 54336 RESERVOIR SIMULATION OF WATERFLOOD PILOT IN NATURALLY FRACTURED SPRABERRY TREND 3

For a two-dimensional case, equations 1,2 and 3 are a setof a system of partial differential equations that lead to fourequations in four unknowns: p1, p2, ux, and uy. The systemwas solved using a fully implicit finite difference schemeand the nonlinear system was solved by using a blockGauss-Seidel approach.

A comparison in performance between a commercial(conventional) dual porosity simulator and a stress dualporosity simulator has been made as shown in Fig. 2. Withconstant permeability-porosity case, both simulators givesimilar result in predicting the reservoir performance.However, in modeling stress-sensitive permeability, theconventional dual-porosity simulator under high productionrates (> 100 bopd) is inadequate. Numerical results alsoshowed that permeability reduction due to stress couldsignificantly reduce well productivity in naturally fracturedreservoirs.

Imbibition MechanismBackground. Imbibition plays a very important role in oilrecovery, during waterflooding in the naturally fracturedSpraberry Area. Imbibition describes the rate of masstransfer between the rock and the fractures, which, in turndepends on wettability of the rock. Therefore, understandingthe imbibition process is crucial. Two imbibitionexperiments were conducted; spontaneous and dynamicimbibition experiments.Spontaneous Imbibition Experiments. Several studieshave been conducted to simulate spontaneous imbibitionexperiments in a core plug using either analytical ornumerical approaches.8-12 In this study, we were concernedprimarily with capillary pressure as the only driving force inthe spontaneous imbibition process. The experiments wereconducted under reservoir condition using core plugs takenfrom the low-permeability Spraberry formation. Spraberryoil and synthetic Spraberry brine were used as wetting andnon-wetting fluids. The work was performed to develop amathematical model for matching the laboratory imbibitiondata. The matching data can be used to study thespontaneous imbibition process in detail and to investigatethe effect of key variables on the imbibition rate.

Numerical Modeling. The mathematical model for thatprocess was derived based on the following assumptions:gravity terms are negligible, capillary pressure is the onlydriving force where total velocity is zero, and fluid and rockare incompressible. The governing equation was obtained asfollows13:

tS

xS

)S(D www ∂

∂−=

∂∂

⋅∇ φ ..............................................(4)

where the non-linear capillary diffusion coefficient isdefined as

w

cwro

ow S

pfk

k)S(D

∂∂

=µ

................................................(5)

Because of the non-linear capillary diffusion coefficient,equation 4 must be solved by numerical methods. A fullyimplicit finite difference scheme was applied to solveequation 4. The core plug was totally immersed in water, soboundary conditions were set to be constant with 100%water saturation. Initial conditions are required to begin thetime step sequence. In this study, initial conditions werespecified equal to initial water saturation. In order to matchthe experimental data, the capillary pressure curve was onlyparameter to be altered.

Figure 3 shows four experimental data and numericalsolution matches for recovery against time, with lowcapillary pressure shown in Fig. 4. The low capillarypressure obtained from this study indicates that theSpraberry cores are weakly water-wet. This finding is alsosupported by the measurement of wettability index (averageAmott index is 0.3). Sensitivity studies on imbibition ratesfor varying capillary pressure, oil and water relativepermeability curves, oil and water viscosity, and initialwater saturation were conducted. We found that the rate ofimbibition is affected less by varying water relativepermeability and water viscosity values.

However, the results from this study suggest that thestatic imbibition experiment may fail to predict theperformance of waterflooding in naturally fracturedreservoirs because of the following reasons: (i) the capillarypressure obtained from this study is very low compared tothe experimental study that was used to generate capillarypressure, and (ii) the static imbibition ignores the viscousforce.

Therefore, dynamic imbibition experiments wereconducted using artificially fractured Spraberry core toillustrate the actual process of waterflooding in naturallyfractured reservoirs. The work was proceeded by numericalmodeling using a commercial black oil simulator (Eclipse)to generate matrix capillary pressure as a result of matchingbetween experimental data and numerical solution.

Dynamic Imbibition Experiments. The dynamicimbibition concept was first introduced by Brownscombeand Dyes (1952).14 However, until now not many studiesfound in the literature on this subject, either experimental ortheoretical.15-17

A coreflood experiment at low injection rate wasperformed under reservoir conditions. The fracture patternon the core sample was generated along the long axis usinga hydraulic cutter. The cut sections were put back togetherwithout polishing the cut surfaces and without spacers. Thematrix face was sealed off to allow brine injection onlythrough the fracture. The fractured core was inserted into theHassler-type core holder. During the experiment, the oil-saturated core was flooded by injecting with constantinjection rate at reservoir temperature and 500 psiaconfining pressure. The oil and brine produced werecollected against time at the producing end of the fracturedcore until zero oil production rate was achieved.

4 E. PUTRA, D.S. SCHECHTER SPE 54336

Numerical Modeling.18 The rectangular grid block wasused to overcome the difficulty of modeling the horizontalcylindrical core shape. Thus, the pore volume of rectangularshape was set equal to that of cylindrical shape.

Single porosity simulation was used instead of dualporosity simulation, because single porosity is morerepresentative for modeling a single fracture from theartificially fractured core. However, this single porositysimulation has to be able to duplicate the behavior of dualporosity simulation, which has different properties formatrix and fracture media. Thus, the properties of fracture,such as porosity, permeability, relative permeability, andcapillary pressure were added into the single porositysimulator.

Three layers were used in the model with the fracturelayer between the matrix layers. In addition, 10 x 10 gridblocks were used in x and y directions. The fracture layerwas injected at one end with constant low water injectionrate. Oil and water were produced at the opposite end of thefracture layer. The rest of the boundary blocks had aspecified no-flow boundary condition. As in thespontaneous imbibition modeling, relative permeability wasfixed and the matrix capillary pressure curve was the onlyparameter adjusted to match the experimental data.Meanwhile, the fracture capillary pressure was set to be zeroand a straight-line relative permeability was used in thefracture layer. Once numerical analysis results satisfactorilymatched the experimental data, then the value of the matrixcapillary pressure obtained was used as a verification of thematrix capillary pressure input of the Humble Pilotsimulation.

The best matches between experimental data andnumerical solutions (only cumulative water production andcumulative oil production are presented) can be seen in theFigs. 5 and 6. The matrix capillary pressure obtained fromthis study is in good agreement with that obtained fromstatic equilibrium experiments (Guo et al.19), as shown inFig. 7.

Analysis of these two issues, stress-sensitivepermeability and imbibition mechanism, appears to behelpful for understanding the reservoir behavior andenhancing the quality and quantity of the simulation data.

Modeling and SimulationBeside the information obtained from the above study,

the information from geological and petrophysical analysisof reservoir cores, core-log integration analysis, fracturecharacterization, well test analysis and extensive data setsavailable on a well-by-well basis, allows us to apply modernsimulation techniques to evaluate the performance of this40-year-old pilot.

The Spraberry Trend was proven productive in February1949, producing predominantly two thin intervals, the 1Uand 5U, in the Upper Spraberry (Fig. 8).20,21 The UpperSpraberry, at an average depth of 7000 ft, has a grossthickness of approximately 220 ft and is composed of sixstacked units (1U-6U). The individual beds rarely exceed 15

ft in thickness. Core analysis and well logging showed thatthe reservoir rock is characterized by both low porosity andlow permeability. Matrix permeabilities are on the order of 1md or less with porosities ranging from 6 to 14 %. The payzones are cut by an extensive system of vertical fractures asshown in Fig. 8. The values of matrix permeability wouldnot be significant without a system of interconnectedvertical fractures that allow oil to flow from the matrixthrough the fractures and to the production wells. Most ofthe oil is stored in the matrix, since fracture porosity is onthe order of 1% or less.

The fracture orientation was obtained by a number ofwell tests, including pulse and interference tests, buildupand fall off tests, and interwell tracer tests. It varies fromarea to area from N36°E to N76°E; however in general, thedirection is approximately N50°E, as shown in Fig. 8.Further measurements were conducted recently by coringthe Upper Spraberry 1U and 5U sands horizontally andperforming tracer slugs on the Midkiff Unit in the Spraberryreservoir.22 Approximately 400 ft of horizontal core wastaken from the two main pay sections. Three distinct naturalfracture orientations are present in these horizontal cores,trending approximately NNE, NE, and ENE.23 Forty-sixcore samples taken from 1U show that the average fracturetrend is in N42°E. Fifty-seven core samples taken from 5Ushow that two fracture trends are present, with the averagefracture trends are 32°NNE and 80°NNE, respectively, asshown in Fig. 8. Four different tracer slugs were injected infour different injection wells. The surrounding productionwells were monitored for a period of 183 days followingtracer injection. Two fracture systems were identified, aprimary fracture system oriented at approximately N38o Eand a secondary fracture system oriented in an east-westdirection.

The magnitude of permeability anisotropy between on-trend and off-trend varies from about 6:1 to 144:1 orhigher.24 The effective permeability of the reservoir asdetermined by pressure build-up tests ranged from 2 to 180mD.25

Fracture spacing is the other important quantitativefracture system parameter that is necessary to predictfracture porosity and permeability in a reservoir. Fracturespacing can be directly quantified and it does not changewhen the reservoir is perturbed. Variation in fracturespacing can have a dramatic effect on fracture permeability.The horizontal cores show that the average fracture spacingin 1U sand is 3.17 ft, while in 5U sand it is 2.7 ft (Fig. 8).

Based on that information, the reservoir model for theHumble Pilot area (Fig. 9) was developed using three-phase,3-D and dual porosity options in Eclipse. Characterization ofthe Humble Pilot and corresponding input were included inthe reservoir model. The dual porosity model was used,since the Spraberry formation is very tight, so no significantfluid flow in the matrix can be assumed. The main flow inthe reservoir occurs through the exchange of fluid from the

SPE 54336 RESERVOIR SIMULATION OF WATERFLOOD PILOT IN NATURALLY FRACTURED SPRABERRY TREND 5

matrix to the fractures and from the fractures towards theproduction wells.

The grid dimension is 22x18 with 396 grid blocks in thehorizontal direction and three grid blocks in the verticaldirection. A total number of 1188 grid blocks were used tosimulate the pilot. The total number of grid blocks becomestwice that of a single porosity realization, since thesimulator generates one set of grid blocks for matrixparameters and one set for the fracture parameters. Thewells and all layers were aligned parallel with the majorfracture system with an orientation of N50°E. Figure 10shows the grid model for the five-spot pattern afterorientation with the major fracture system. The virginreservoir properties are shown in Table - 1. The reservoirfluid analysis report was conducted by Magnolia PetroleumCo.26 as displayed in Table - 2.

The fluid samples were recombined and flashed toreservoir conditions at a temperature of 140°F. It was foundthat the saturation pressure was 1840 psia, 460 psia belowthe estimated original reservoir pressure of 2300 psi.

The two main zones, the 1U and 5U, were modeled withone large intervening shale layer. It was assumed that therewas no vertical communication in the matrix and fracturebetween the two different sand zones, by setting thetransmissibilities of matrix and fracture in the interveningshale to be zero. This assumption agrees with recenthorizontal core analysis.23

Since regional fractures are primarily oriented in onedirection, the on-trend fracture permeability is set to bedifferent from the off-trend fracture permeability. The ratiofracture permeability is 15:0.25. The matrix permeability isset to be 0.02 md. The difference between off-trend fracturepermeability and matrix permeability is taken into accountfor cross fractures in the model.

The five-spot with one producer (Sh. B-9) and fourinjectors (Sh. B-2, Sh. B-4, Sh. B-6 and Sh. B-10) weremodeled in the simulation. Straight lines connecting the fourinjection wells confined the 80-acre pilot area.

In addition to the five-spot wells, five observation wells:Sh. B-1, Sh. B-5, Sh. B-7, Sh. B-11, T-1, A-4 and Sh. B-8,were included to provide information on the changes inreservoir pressure and production rates. These wells mighthelp in tracing the response of the flood outside the pattern.

In order to match the observed data from the middleproducer, Sh. B-9, sensitivity cases were performed toevaluate ranges of behavior for different values to help assesthe impact of major uncertainties on predictedperformances.

A fracture spacing of 2.86 ft was used to history-matchthe observed field data performance. Decreasing the fracturespacing increases the shape factor value; hence, thetransmissibility from matrix to fracture increases andtherefore, the oil production rate increases.

Reservoir permeability was much greater in the majorfracture trend than in the minor direction. A fracturepermeability ratio of 15:0.25 between major (Kxf) and minor

permeabilities (Kyf) and the matrix permeability of 0.02 mdwere used. We input different values for matrix and minorfracture permeabilities to account for cross-fractures. Waterproduction rate increases with an increase in the minorfracture permeability, while increasing major permeabilityincreases the oil rate.

The relative permeability used in this study is shown inFig. 11. It is very difficult to accurately measure fracturepermeability curves for a reservoir. The assumption for thiscurve is that both phases are equally mobile for the entirerange of saturations for the fractures. It was observed thatalteration of relative permeability curves in the fracturesystem does not significantly change the results.

A fracture porosity of 0.1% was used in the model.Using a fracture porosity 1.0%, not much water wasproduced because most of the water stayed in the fracturerock instead of flowing to the well. The matrix porosity waskept constant at 10%. Increasing matrix porosity increasesoil in the matrix block, and therefore, oil recovery.

The major fracture direction is oriented approximatelyN50°E. Two additional simulations were conducted toinvestigate the effects of rotation of the major fractureorientation. The orientations simulated were N60°E andN85°E. Both these simulations resulted in too-high waterproduction in the middle producer, since the well at theseorientations was aligned with east and west water injectors.

After those sensitivities studies, an attempt was made tomatch the observed data for the middle producer, Sh. B-9.The numerical results shows good agreement with observeddata, as shown in Figs. 12 through 15, using the parameterslisted in Tables 3 and 4. The trend of oil and gas rates issimilar because straight-line relative permeability curves inthe fracture were used. The peak in the gas production rateobserved in the field upon initiation of water injection isdifficult to obtain in the numerical results. Several effortswere conducted to match that peak but it seems impossibleto match the very high gas production rates. Although thegas peak cannot be matched, most of that rate shows goodmatches with numerical results.

The bottomhole pressure for the middle producer wasstrongly dependent on the rates of surrounding observationwells and the ratio of fracture permeability. Therefore, theratio of fracture permeability was altered to matchproduction and pressure histories. The pressure-sensitiveoption was also applied to model stress-sensitivepermeability. This option was used as an additionalparameter to match the simulated bottomhole pressure. Theuse of this option is valid due to low production rate ofHumble wells.

Methods to Increase Efficiency of Waterflooding inNaturally Fractured ReservoirsHorizontal Well. Recent research on horizontal wells hasfocused increasingly on fractured reservoirs. One of theresearch objectives is to increase horizontal wellproductivity compared to that obtained with vertical wells.

6 E. PUTRA, D.S. SCHECHTER SPE 54336

Due to its length, often much greater than that of a verticalwell, a horizontal well can intercept many more fissuresthan a vertical well, thus obtaining higher productivity.

Since the average reservoir pressure in the SpraberryTrend Area is different from area to area, the averagereservoir pressure was varied from 1000 psia to 1500 psiawith different lengths of horizontal well sections. Thesimulations were performed using a constant plateau rate of100 BOPD, no water injection, and 500 psi bottomholepressure for 10 years. These simulations were by no meansoptimized, but performed to illustrate the potential benefitsassociated with horizontal wells in the Spraberry oilprovince. The simulation result is shown in Fig. 16.

The horizontal production well represents a significantimprovement over the vertical production wells. The use ofa horizontal production well could result in three to fivetimes more cumulative oil production than that obtainedusing a vertical production well. Thus, horizontal productionwells could reduce the number of wells by a factor of two.In addition, the cost of a horizontal production well typicallyis only 1.2 to 1.5 times that of a vertical production well (perfoot drilled). The simulation results clearly indicate thebenefit of using horizontal production wells in the SpraberryTrend Area.

The simulation result also suggested that maintaining orincreasing the average reservoir pressure is critical.Increasing the average reservoir pressure by 250 psia wouldalmost double the oil production rate. The pressure can bemaintained or increased by injecting water perpendicular tothe fracture direction (staggered line drive pattern). Thispattern will also delay the water breakthrough in theproducing wells.Well Injectivity Optimization. Elkin27 found that over-injection might have been responsible for low recovery inthe Spraberry area. He showed that the water breakthroughwas characteristic of the Spraberry at the stage of depletionand at high water injection rates. Schechter et al.2 alsomentioned that after waterflooding was initiated in theHumble Pilot test, water breakthrough occurred in mostproducing wells.

Several simulation cases were performed to test thesehypotheses. As a base case, a vertical well with naturaldepletion was run followed by a case using injection wells.The water injection rate from each well varied from 100 to1000 stbw/d. These simulations were run for 10 years with500 psia BHP and 600 psia average reservoir pressure.

The size of the reservoir model was reduced to 40-acrecompared to the 80-acre Humble pilot model, in order toaccelerate the CPU running time. The grid dimension was15 x 15 x 3 and the pattern was set up to be a staggered linedrive pattern.

Figure 17 shows the effect of the vertical productionwell with and without the vertical injection wells on the oilproduction rate. The initial oil rate of 12 bbls/d wasproduced with natural depletion and only 8 bbls/d averageoil rate afterward. The water was injected 1000 stbw/d perwell from four vertical injection wells. At about 1.5 years

after initiation, the water started to sweep oil to theproduction well until the production rate peaked at 50 bopd.As water was produced, the oil rate decreased sharply tozero oil production rate by about eight years. Thecumulative oil production for the injected case was doublethat of the case without injection.

The effect on the oil production rate of the horizontalproduction well with and without the vertical injection wellsis displayed in Fig. 18. The horizontal well section was setat a 500 ft length perpendicular to the fracture direction.Two cases were run, natural depletion (without injectionwells) and waterflooding (with injection wells). In thenatural depletion case, the use of a horizontal productionwell increased cumulative oil production four times overthat predicted by the vertical production well. At the initialtime, 75 bopd was produced, 6.25 times more than thatproduced by the vertical well. As in the case of a verticalproduction well, the production rate from the horizontalproduction well decreased as pressure decreased. However,the oil production rate declined much faster because of ahigher pressure drop than in the vertical well case.

In the waterflooding case, four vertical injection wellswere used. The water started sweeping oil after six months,producing faster than a vertical production well. This isbecause the horizontal production well had a larger drainagearea. Production peaked at 100 bopd for about one year.

The oil peak rate was also longer than from a verticalproduction well because the horizontal production wellsweeps the oil bank from the fracture more uniformly,causing a delay in water breakthrough. Using a horizontalproduction well with vertical injection wells could recoveroil almost 30% over recovery obtained without injectionwells.

In addition to setting the horizontal section perpendicularto the fracture direction, a case using a parallel to thefracture direction was also performed. However, the oilproduction rate was lower, recovering 25% less oil than inthe case of the horizontal well with natural depletion (Fig.18). The poor performance was because the horizontalproduction well did not intersect with the matrix rock, andtherefore, the pressure drop could not be maintained. Theeffect of water injection on oil rate was observed at the sametime as it was for the vertical production well, because ofthe similar distance to the vertical injection wells.

The simulation results from vertical and horizontalproduction wells with vertical injection wells show that it iscrucial to optimize the water injection rate in order to delaywater breakthrough in naturally fractured reservoirs. Twooptimizations can be applied; either by reducing theinjection rate or by using a cyclic waterflood. This studywill be discussed later.

For the next scenarios, the performances of vertical andhorizontal production wells were compared by usinghorizontal injection wells. Only two horizontal injectionwells were opened. The horizontal injection wells wereparallel to the fracture direction because the injection wellsshould push the oil from the matrix to the fractures (forced

SPE 54336 RESERVOIR SIMULATION OF WATERFLOOD PILOT IN NATURALLY FRACTURED SPRABERRY TREND 7

imbibition) and to the production well. Figure 19 shows thatalthough the oil peak rates were lower in both vertical andhorizontal production wells, the high production rates weremaintained longer and the cumulative oil productions werehigher than those obtained by using vertical injection wells.The response of water injection was delayed because bothvertical and horizontal injection wells used the same waterinjection rate (1000 stbw/d).

Several simulations were conducted to optimize thewater injection rate for both vertical and horizontal injectionwells. The water injection rate for each injection well wasvaried from 100 stbw/d to 1000 stbw/d. The simulationswere run until zero oil production occurred and thecumulative production rate from each injection rate wasrecorded, as shown in Figs. 20 and 21.

For the constant injection rate case, the simulationresults show that the optimum injection rate for each verticalinjection well to produce the maximum cumulative oilproduction (235.751 MSTB) from the horizontal productionwell is 200 stbw/d. Using 400 stbw/d injection rate for eachhorizontal injection well, the horizontal production wellproduced 221.048 MSTB cumulative oil production. Thus,the horizontal production well with the vertical injectionwell could produce 15 MSTB higher than that withhorizontal injection wells. However, the injection rate fromthe vertical injection well was more sensitive than that fromthe horizontal injection well. For instance, when the highinjection rate (above 500 stbw/d) was used, the cumulativeoil production from the horizontal production well withhorizontal injection wells was significantly higher than thatwith vertical injection wells.

This study has shown that using vertical injection wellswith high injection rates (greater than 500 stbw/d per well)is not successful in the 40-acre fractured Spraberryreservoir. Study results show that the optimum injection ratefor a horizontal injection well is about twice that of avertical injection well.Cyclic Waterflooding. The difference between naturaldepletion and waterflooding performance, as previouslydiscussed, led to the use of a cyclic operation. Sincereservoir pressure declines rapidly due to production, waterinjection is required to restore the pressure and is followedby producing a well without any water injection.

This cyclic operation was performed to observe theeffect on the oil production rate. Two cyclic schemes wereconducted; the cyclic rate scheme of 2:2 and the cyclic ratescheme of 1:2. The cyclic rate scheme of 2:2 means twoyears producing without waterflood, followed by producingwith a waterflood for the next two years. The results of thecyclic rate schemes were compared to constant injection rateresults as shown on Figs. 20 and 21. The simulation resultsshow that the cyclic rate scheme of 1:2 gave the highestcumulative production rate, followed by the cyclic ratescheme of 2:2 and the constant injection rate. This isbecause cessation of water injection permits capillary forceto hold much of the water in the rock. During pressurereduction, capillary force aids in the expulsion of oil from

the matrix into the fractures (a similar concept was alsoproposed by Elkins27).

ConclusionsThe major conclusions can be drawn as follows:1. It has been shown that conventional dual porosity with

variable permeability cannot be used to model highproduction rates.

2. The stress-transfer effect in naturally fracturedreservoirs was shown to be important.

3. Low imbibition capillary pressure was generated fromthe model in order to match the experimental data.Laboratory experiments indicate that the wettability ofthe core plug was weakly water-wet.

4. The rate of imbibition was not sensitive to waterrelative permeability and water viscosity.

5. This study has shown that spontaneous imbibitioncannot be used to illustrate the actual process ofwaterflooding in naturally fractured reservoirs.

6. Capillary pressure (Pc) obtained from dynamicimbibition modeling was used as verification of Pc usedin the Humble Pilot simulation.

7. Use of horizontal production wells could increasecumulative oil production by three to five times,compared to vertical production wells in the Spraberryformation.

8. Increasing the average reservoir pressure wouldsignificantly increase the oil production rate.

9. A horizontal production well surrounded by verticalinjection wells could give higher cumulative oilproduction than that obtained with horizontal injectionwells, if the injection rate can be optimized. However,the production rate with vertical injection wells is moresensitive than that of horizontal injection wells.

10. High water injection (greater than 500 STBW/D perwell) using vertical injection wells with a constantinjection scheme is not successful in a 40-acre fracturedSpraberry reservoir.

11. Optimization of the injection rate is important prior toconducting waterflooding in naturally fracturedreservoirs.

Nomenclatureb = porosity-compressibility coefficients, LT2M-1

c = compressibility, LT2M-1

D = diffusion coefficients, ML3T-2

e = volumetric strain, dimensionlessE = Young’s modulus, ML-1T-2

f = fractional flow, dimensionlessG = shear modulus, ML-1T-2

k = permeability, L2

kr = relative permeability, dimensionlessp = fluid pressure (+ for compression), ML-1T-2

Pc = capillary pressure, ML-1T-2

S = saturation, fractiont = time, Tu = displacement, L

8 E. PUTRA, D.S. SCHECHTER SPE 54336

v = poisson ratio, dimensionless

Subscriptsb = bulkc = confining

eff = effectivef = fluid

i,j = integer denoting cell location in the x- and y-directions.

n = index of primary and secondary poreso = oilp = pores = solidt = totalt = time

w = water1 = primary pores2 = secondary pores

Superscripts* = single porosity nonfractured system

Greekα = effective stress coefficient associated with the

bulk volumetric change,dimensionlessβ = effective stress coefficient associated with the

pore volumetric change, dimensionlessδi j = Kronecker’s delta (δij =1 for i=j, δij=0 for i≠j)

ε = strain, dimensionlessφ = porosity, fractionΓ = interporosity flow, L3/T/L3

µ = fluid viscosity, ML-1T-1

ν = Poisson’s ratio, dimensionlessρ = fluid density, ML-3

σ = shape factor, L-2

∇ = gradient∇⋅ = divergence

AcknowledgementsThis work was financially supported by the United StatesDepartment of Energy's National Petroleum TechnologyOffice under Contract No. DE-FC22-95BC14942. Supportfrom the following companies is gratefully acknowledged:Chevron, Martahon Oil Co., Mobil Research andDevelopment Corp., Mobil E&P USA, Pioneer NaturalResources (formerly Parker and Parsley Petroleum Co.),Petroglyph Operating Co., Texaco E&P Technology Dept.,The Wiser Oil Co. and Union Pacific Resources. GeoQuestdonated software to New Mexico Petroleum RecoveryResearch Center and used in reservoir simulation is alsogratefully acknowledged.

References1. "Waterflood Possibilities Spraberry Trend Area Field," Sohio

Production Company, (Sep. 1957).2. Schechter, D.S., McDonald, P., and Sheffield, T.: “Reservoir

Characterization and CO2 Pilot Design in the NaturallyFractured Spraberry Trend Area, ” paper SPE 35469 presentedat the 1996 SPE Permian Basin Oil and Gas Recovery,Midland, March 27-29.

3. Huyakorn, P.S. and Pinder, G.: Computational Methods inSubsurface Flow, Academic, San Diego, CA (1983), 229-288.

4. Unger, D.J. and Aifantis, E.C.: “Notes: Completeness ofSolutions in Double Porosity Theory,” Acta Mechanica(1988) 75, 269-274.

5. Bai, M., Elshworth, D., and Rogiers, J.C.: “Modeling ofNaturally Fractured Reservoirs Using Deformation DependentFlow Mechanism,” Int. J. Rock Mech. Min. Sci. & Geomech.(1993), 1185-1191.

6. Chen, H.-Y. and Teufel, L.W.: "Coupling Fluid Flow andGeomechanics in Dual-Porosity Modeling of NaturallyFractured Reservoirs," paper SPE 38884 presented at the 1997SPE Annual Technical Conference and Exhibition, SanAntonio, Oct. 5-8.

7. Putra, E., Chen, H.Y., Teufel, L., and Schechter, D.S.:"Numerical Modeling of Solid Deformation and Stress-dependent Permeability in Naturally Fractured Reservoirs,"paper included in the annual report, "Advanced ReservoirCharacterization and Evaluation of CO2 Gravity Drainage inthe Naturally Fractured Spraberry Trend Area," (DOEContract No.: DE-FC22-95BC14942), Oct., 1998.

8. Baker, R. and Wilson, G.: "Numerical Simulation ofLaboratory Scale Imbibition Experiment," Internal ReportEpic Consultant Services Ltd., (April 1997).

9. Bech, N., Jensen, O.K., and Nielsen, B.: "Modeling ofGravity-Imbibition and Gravity-Drainage Processes," SPERE(Feb. 1991), 129-136.

10. Beckner, B. L., Ishimoto, K., Yamaguchi, S., Firoozabadi, A.,and Azis, K.: "Imbibition-Dominated Matrix-Fracture FluidTransfer in Dual Porosity Simulators," paper SPE 16981presented at the 1987 SPE Annual Technical Conference andExhibition, Dallas, Sept. 27-30.

11. Blair, P.M.: "Calculation of Oil Displacement byCountercurrent Water Imbibition," SPEJ (Sept. 1964), 195-202; Trans., AIME (1964) 231.

12. Chen, J., Miller, M.A., and Sepehrnoori, K.: "TheoreticalInvestigation of Countercurrent Imbibition in FracturedReservoir Matrix Blocks," paper SPE 29141 presented at the1995 SPE Symposium on Reservoir Simulation, San Antonio,Feb. 12-15.

13. Putra, E., Fidra, Y., and Schechter, D.S.: "SpontaneousImbibition Modeling of Spraberry Core Plugs Using aNumerical Finite Difference Scheme," paper submitted to the2nd Quartely Report (DOE Contract No.: DE-FC22-95BC14942), PRRC No. 24-98 (June 1998).

14. Brownscobe, E.R. and Dyes, A.B.: “Water-ImbibitionDisplacement-A Possibility for the Spraberry,” Drill. andProd. Prac. API (1952), 383-390.

15. Graham, J.W. and Richardson, J.G.: "Theory and Applicationof Imbibition Phenomena in Recovery of Oil," Trans., AIME(1960) 216, 377.

16. Kleppe, J. and Morse, R.A.: "Oil Production from FracturedReservoirs by Water Displacement," paper SPE 5084presented at the 1974 SPE Annual Meeting, Houston, Oct. 6-9.

SPE 54336 RESERVOIR SIMULATION OF WATERFLOOD PILOT IN NATURALLY FRACTURED SPRABERRY TREND 9

17. Babadagli, T.: “Injection Rate Controlled Capillary ImbibitionTransfer in Fractured Systems,” paper SPE 28640 presented atthe 1994 SPE Annual Technical Conference and Exhibition,New Orleans, Sept. 25-28.

18. Putra, E., Fidra, Y., and Schechter, D.S.: "Dynamic ImbibitionModeling of Artificially Fractured Core Using a NumericalSimulator," paper included in," Advanced ReservoirCharacterization and Evaluation of CO2 Gravity Drainage inthe Naturally Fractured Spraberry Trend Area," annual report,Contract No. DEFC2295BC14942, U.S. DOE (1998).

19. Guo, B., Schechter D.S., and Baker, O.R.: "An IntegratedStudy of Imbibition Waterflooding in Naturally FracturedSpraberry Trend Area Reservoirs," paper SPE 39801presented at the 1998 SPE Permian Basin Oil and GasRecovery Conference, Midland, Texas, March 25 - 27.

20. Banik, A.K. and Schechter, D.S.: "Characterization of theNaturally Fractured Spraberry Trend Shaly Sands Based onCore and Log Data," paper SPE 35224 presented at the 1996Permian Basin Oil and Gas Recovery Conference, Midland,Texas, March 27-29.

21. Schechter, D.S. and Banik, A.K.: "Integration ofPetrophysical and Geological Data with Open-Hole Logs forIdentification of the Naturally Fractured Spraberry PayZones," paper SPE 38913 presented at the 1997 SPE AnnualTechnical Conference and Exhibition, San Antonio, Texas,October 5-8.

22. Baker, R. and Spencely, N.: “Analysis of Tracer Study at TheMidkiff Unit Upper Spraberry Formation,” Internal EpicConsulting Ltd., Calgary, Canada (Aug. 1996).

23. McDonald, P., Lorenz, J., Sizemore, C., Schechter, D.S., andSheffield, T.: "Fracture Characterization Based on OrientedHorizontal Core from the Spraberry Trend Reservoir: A CaseStudy," paper SPE 38664 presented at the 1997 SPE AnnualTechnical Conference and Exhibition, San Antonio, Oct. 5-8.

24. Elkins, L.F. and Skov, A.M.: “Determination of FractureOrientation from Pressure Interference,” Trans., AIME (Oct.1960) 219, 301-304.

25. Dyes, A.B. and Johnston, O.C.: “Spraberry Permeability fromBuild-Up Curve Analyses,” Trans., AIME (1953) 198, 135-138.

26. "PVT Analysis Report, Louise Schackelford No. 1, SpraberryReservoir, Tex Harvey Field", Petroleum ProductionLaboratories Inc. (May 30, 1952).

27. Elkins, L.F.: “Cyclic Water Flooding the Spraberry Utilizes'End Effect' to Increase Oil Production Rate,” JPT (August1963), 877-884.

Table 1—RESERVOIR PROPERTIES FOR THEHUMBLE PILOT FLOOD

Original Reservoir Pressure, psia 2300Saturation Pressure, Psia 1840Reservoir Temperature, °F 140Initial Water Saturation, % 30-35Initial Oil Saturation, % 65-70Matrix Porosity, % 6 - 18

Effective Permeability, mD 2.0-183.0Matrix Permeability; mD;AreaVertical

0.1 - 0.50.05-0.25

Pore Compressibility, psi-1 4.00E-6

TABLE 2 —RESERVOIR FLUID PROPERTIES

Oil Formation Volume Factor, gm/cc 1.385Density of Residual Oil, gr/cc 0.851Molecular Weight of Residual oil 217Stock Tank Oil Gravity, °API 37.8Gas Specific Gravity 0.932Density of Stock Tank Water, gr/cc 1.010Water Formation Volume Factor, bbl/STB 1.003Water Viscosity, cp 1.2486Water Compressibility, psi-1 3.00E-6

TABLE 3—MATCHED PARAMETERS FOR MATRIX

Property Symbol Value

Porosity φm 10.0 %Permeability in the x-direction Kx 0.02 mdPermeability in the y-direction Ky 0.02 mdPermeability in the z-direction Kz 0.02 md

TABLE 4—MATCHED PARAMETERS FOR FRACTURES

Property Symbol Value

Porosity φf 0.1 %Fracture Permeability Ratio kxf/kyf 15/0.25Shape Factor σ 1.47Major Fracture Orientation - N50°E

10 E. PUTRA, D.S. SCHECHTER SPE 54336

Fig. 1—The unitized portion of the Spraberry Trend Area,showing the location of the Humble pilot area.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1.0E+00 1.0E+02 1.0E+04 1.0E+06 1.0E+08

Time (Sec)

Vol

um

e O

il (

cc)

Numerical SolutionSPR-8HSPR-9HSPR-7HRSPR-11H

Fig. 3—Matching between spontaneous-imbibition experimentswith numerical solution.

0

500

1000

1500

2000

2500

3000

3500

0 50 100 150 200 250 300 350

Oil production rate (STB/D)

Wel

lbo

re f

low

ing

pre

ssu

re (

Psi

a)

conventional dual-porosity stress dual-porosity

variable perm and por (conv) variable porm and por (stress)

Fig. 2—Comparison of performance between conventional andstress dual-porosity simulators.

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.300 0.350 0.400 0.450 0.500 0.550 0.600

Sw (fraction)

Pc

(psi

a)

SPE 54336 RESERVOIR SIMULATION OF WATERFLOOD PILOT IN NATURALLY FRACTURED SPRABERRY TREND 11

Fig. 4—Imbibition capillary pressure obtained from matchingspontaneous imbibition data.

Fig. 5—Matching between experimental data and the numericalsolution (Spraberry core - cumulative water production).

0

5

10

15

20

25

30

0.0 0.2 0.4 0.6 0.8 1.0

Water Saturation (PV)

Ca

pil

lary

Pre

ssu

re (

psi

g)

Pc detemined by laboratory experimentPc determined by numerical simulation

Fig. 7—Comparison between capillary pressure obtained from

numerical simulation and laboratory experiment (Spraberrycore).

Fig. 6—Matching between experimental data and the numericalsolution (Spraberry core - cumulative oil production).

Spraberry FractureSystem Schematic

Average fracture spacing3.17 ft (N42E) Ì

Average two sets of fracture spacing1.62 and 3.8 ft (N32E and N80E)

Ì

Shale Layer(140 ft)

Sand Layer1U (10 ft)

Sand Layer5U (15 ft)

Pay zone, 5USiltstone,

Vshl<15%,φ>7%

Pay zone,1USiltstone,

Vshl<15%,φ>7%

Non-pay zone,2U,3U, and 4U

Siltstone+Dolomite,

Vshl<15%, φ <7%

Fig. 8—The Spraberry fracture system schematic.

12 E. PUTRA, D.S. SCHECHTER SPE 54336

Fig 9—Humble pilot test showing that the center productionwell increased by over 250 bopd after waterflooding. The wellsin the outside of the pattern influenced by injected water fromthe pilot wells can be seen to occur along the fracture trend.

Oil-gas Relative Permeability

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

So

Kr

Kro (fracture) Krg (fracture)

Kro (matrix) Krg (matrix)

N15O

N50OEFracture Trend

8

9

10

17

16

15

20

21

22

B-9

B-2

B-4

B-6

B-10B-5

B-3

A-4

B-11B-8

T-1

B-1

B-7

Fig 10—Grid model is oriented to N50°E along the majorfracture system.

Oil-water Relative Permeability

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sw

Kr

Krw (farcture) Kro (fracture)

Krw (matrix) Kro (matrix)

SPE 54336 RESERVOIR SIMULATION OF WATERFLOOD PILOT IN NATURALLY FRACTURED SPRABERRY TREND 13

Fig. 11—Matrix and fracture relative permeabilities.

Fig. 12—Match of observed data and simulated data for oilproduction rate.

Fig. 14—Match of observed data and simulated data for gasproduction rate.

Fig. 13—Match of observed data and simulated data for waterproduction rate.

Fig. 15—Match of observed data and simulated data for bottomhole pressure.

14 E. PUTRA, D.S. SCHECHTER SPE 54336

0

50

100

150

200

250

300

350

400

500 700 900 1100 1300 1500 1700 1900

Average Reservoir Pressure, Psia

CO

P, M

ST

B

vertical 350 ft 525 ft745 ft 1050 ft

Fig. 16—Effect of average reservoir pressure on cumulative oilproduction.

Fig. 18—The effect of a horizontal production well with and

without vertical injection wells on the oil production rate.

Fig. 17—The effect of a vertical production well on the oilproduction rate.

Fig. 19—The effect of vertical and horizontal production wells

Major FractureTrend

Major Fracture Trend

Major Fracture Trend

Major Fracture Trend

Major Fracture Trend

Major Fracture Trend

Major Fracture Trend

Major Fracture Trend

SPE 54336 RESERVOIR SIMULATION OF WATERFLOOD PILOT IN NATURALLY FRACTURED SPRABERRY TREND 15

with horizontal injection wells on the oil production rate.

150

175

200

225

250

275

300

0 200 400 600 800 1000 1200

INJECTION RATE (STBW/D)

CO

P (

MS

TB

)

constant inj. rate cyclic rate (2 : 2)

cyclic rate (1 : 2)

Fig. 5.20 – The effect of a horizontal production well withvertical injection wells and different injection schemes oncumulative oil production.

150

175

200

225

250

275

300

0 200 400 600 800 1000 1200

INJECTION RATE (STBW/D)

CO

P (

MS

TB

)

constant inj. rate cylic rate (2 : 2)

cylic rate (1 : 2)

Fig. 5.21 – The effect of a horizontal production well withhorizontal injection wells and different injection schemes oncumulative oil production (note: the cumulative oil productionis lower than that shown in the previous figure).

Major Fracture Trend

Major Fracture Trend

16 E. PUTRA, D.S. SCHECHTER SPE 54336